Is the Euclidean topology on $\mathbb{R}$ contained in a maximal connected topology?

Question

If $(X,\tau)$ is a connected space, then $\tau$ need not be contained in a maximal connected topology.

Is the Euclidean topology on $\mathbb{R}$ contained in a maximal connected topology?

Answer 1

Yes, see Maximal connected expansions of the reals by J. A. Guthrie, H. E. Stone and M. L. Wage, Proc. Amer. Math. Soc. 69 (1978), 159-165.